Sorry I wasn’t clear.
We are NOT talking about what a professional print shop would do, as they have access to large printing presses and large sheets of paper (this is why they can do “8-up” or “16-up” – where they print 8 book page images on one side of a large sheet of paper, and print 8 more on the back; the double-sided sheet is then folded in a particular way that puts all the pages in the correct order, and the outside edges are then trimmed).
Nope, we are not talking about that. We are talking about a way to make it simple for a photocopy shop to hand folded large books.
I’ll try to explain it again:
We have hymnals, dictionaries, and shellbooks which are formatted to print on A5 sheets of paper (half of an A4 sheet).
We export these books to a PDF file and then to PDF Droplet to lay up the BOOK PAGES, side-by-side, 2 per side on A4 paper.
So far, this is all normal for PDF Droplet.
Problem with LARGE BOOKS:
PDF Droplet only lays out the pages sequentially, which means the very LAST page of the book ends up printed next to the FIRST page of the book on the first sheet printed. This is okay when the book is short, like up to 30 book-pages. Above 30 book-pages though, and the folded sheets have to fold around more and more sheets of paper, making the book fat, and the finished book’s outside edge beveled; not flush.
Solution for bigger books:
Give PDF Droplet the ability to lay out LARGE BOOKS, with the BOOK pages organized in 4-page chunks, i.e., ONE SHEET of PRINTED A4 PAPER holds 2 BOOK PAGES per SIDE = 4 book pages/printed sheet of paper.
So, the sequence of the BOOK pages on the SHEET SIDES is this:
Page 4 | Page 1 <= FRONT SIDE OF 1st A4 SHEET
Page 2 | Page 3 <= BACK SIDE OF 1st A4 SHEET
Page 8 | Page 5 <= FRONT SIDE OF 2nd A4 SHEET
Page 6 | Page 7 <= BACK SIDE OF 2nd A4 SHEET
Page 12 | Page 9 <= FRONT SIDE OF 3rd A4 SHEET
Page 10 | Page 11 <= BACK SIDE OF 3rd A4 SHEET
Etc.
See? This gives us 4 pages per printed sheet (2/side, front and back)
How is it used:
- Each printed A4 sheet is then folded in half (i.e. p2 on p3; p6 on p7; p10 on p11, etc.).
- Each folded sheet is laid on top of the last one (face down).
- Last sheet contains the last 4 pages of the book and, when folded and stacked on the pile, finishes the book.
- This creates a stack of folded sheets (NOT a folded booklet)
- The stack of folded sheets is then stabled through front to back, near the spine, in two or three places, to hold the sheets together. (NOTE: the original book needs to be formatted to allow for stables in the “gutter margin” with mirrored margins—larger inside margins than outside margins.)
- A cover is then glued on the outside.
- The result is a nice, crisp, flush-edged book.
And YES, you are correct, it is a VERY SMALL “Sub-booklet”; it is a SINGLE SHEET sub-booklet. 
Again, this has nothing to do with professional printing shops with real presses. This is just a way for a small, non-professional, photocopy shop to make books that are nice, without them getting really confused as to where each sheet needs to go.
The professional “sub-booklet” you quote from Oxford Uni Press is used in hardback library books. It is MUCH more complex (where each sub-booklet is printed on huge sheets of paper, folded, cut, and then sewn through the folded spine of each sub-booklet—to hold the pages of each sub-booklet together—then the sub-booklets are stacked and sewn again to a fabric backing, which is then glued to stiff endpapers and then glued to the hardcover itself). No, we are NOT going down THAT road!
Ours is a simple need, but to make PDF Droplet usable to a wider audience, it might be good if the user could specify their particular “sub-booklet” needs: providing a way for users to tell PDF Droplet how many book-pages they want on each side of the printed sheet of paper, and how many book-pages they want total in each sub-booklet.
- Ours would be 2/side on A4, with 4/booklet (which would yield double-sided sub-booklets of one printed sheet each)
- A modest printshop might want 2/side on A4, 16/booklet (which would yield sub-booklets of 8 double-sided printed sheets per folded sub-booklet)
- A professional shop might want 8/side on A1 paper, with 16/booklet (which would yield a sub-booklet of ONE printed A1 sheet, but this sheet is huge, and they would then fold it and cut it to make a sub-booklet of 16 pages, like we see in library books). NOTE: I don’t think this option needs to be supported by PDF Droplet, as anyone able to print on A1 paper will have professional software to handle the lay up.
Does this make sense now? I can send examples and photos if it still isn’t clear.
Thanks for asking,
David C
Indonesia
Again, this has nothing to do with professional printing shops with real presses. This is just a way for a small, non-professional, photocopy shop to make books that are nice, without them getting really confused as to where each sheet needs to go.